Albert Barnes —
Cliff Barnes —
Jake Barnes —
Wednesday, May 10, 2023
Puzzle Begun: Barnes Foundations
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Thursday, December 29, 2022
Bullshit Studies: “Foundations of Modern Consciousness”
The first Romantics
"How a close group of brilliant friends,
in a tiny German university town, laid
the foundations of modern consciousness"
— Headline for the article whose URL is . . .
https://aeon.co/essays/
english-romanticism-was-born-from-a-serious-germanomania
The article was published by Aeon on December 20, 2022,
and is featured in today's Arts & Letters Daily . On the author:
"Andrea Wulf is a historian and the award-winning author
of several books, including the bestselling
The Invention of Nature (2015) and, most recently,
Magnificent Rebels: The First Romantics and
the Invention of the Self (2022). She is a Miller Scholar
and a Fellow of the Royal Society of Literature."
Related material — "The Eight" According to Coleridge.
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Saturday, June 25, 2022
For Harlan Kane: The Thoreau Foundation
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Wednesday, January 13, 2021
Foundational Securities
“… I’m reverting to the foundational securities of childhood . . . .”
— University Diaries weblog this morning
Among my foundational securities is an image that might be titled . . .
The Truman Show —
Related literary remarks — Moss on the Wall.
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Friday, March 13, 2020
Tuesday, April 16, 2019
Saturday, November 3, 2018
Foundations of Geometry
"costruire (o, dirò meglio immaginare) un ente" — Fano, 1892
"o, dirò meglio, costruire" — Cullinane, 2018
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Thursday, June 4, 2015
Foundations
Princeton University's president on June 2, 2015 —
“Dream Audaciously,” Eisgruber Urges Graduates
Related news —
Film director Christopher Nolan at Princeton on June 1, 2015:
“In these graduation speeches, generally, you have the
speaker say something along the lines of, ‘You need to
chase your dreams,’ ” Nolan said. “But I’m not going to
say that because I don’t believe it. I don’t want you to
chase your dreams. I want you to chase your realities.
And I want to say: Don’t chase your realities at the
expense of your dreams, but as the foundation of your
dreams.”
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Sunday, May 31, 2015
Saturday, October 25, 2014
Foundation Square
In the above illustration of the 3-4-5 Pythagorean triangle,
the grids on each side may be regarded as figures of
Euclidean geometry or of Galois geometry.
In Euclidean geometry, these grids illustrate a property of
the inner triangle.
In elementary Galois geometry, ignoring the connection with
the inner triangle, the grids may be regarded instead as
illustrating vector spaces over finite (i.e., Galois) fields.
Previous posts in this journal have dealt with properties of
the 3×3 and 4×4 grids. This suggests a look at properties of
the next larger grid, the 5×5 array, viewed as a picture of the
two-dimensional vector space (or affine plane) over the finite
Galois field GF(5) (also known as ℤ5).
The 5×5 array may be coordinatized in a natural way, as illustrated
in (for instance) Matters Mathematical , by I.N. Herstein and
Irving Kaplansky, 2nd ed., Chelsea Publishing, 1978, p. 171:
See Herstein and Kaplansky for the elementary Galois geometry of
the 5×5 array.
For 5×5 geometry that is not so elementary, see…
-
"The Hoffman-Singleton Graph and its Automorphisms," by
Paul R. Hafner, Journal of Algebraic Combinatorics , 18 (2003), 7–12, and -
the Web pages "Hoffman-Singleton Graph" and "Higman-Sims Graph"
of A. E. Brouwer.
Hafner's abstract:
We describe the Hoffman-Singleton graph geometrically, showing that
it is closely related to the incidence graph of the affine plane over ℤ5.
This allows us to construct all automorphisms of the graph.
The remarks of Brouwer on graphs connect the 5×5-related geometry discussed
by Hafner with the 4×4 geometry related to the Steiner system S(5,8,24).
(See the Miracle Octad Generator of R. T. Curtis and the related coordinatization
by Cullinane of the 4×4 array as a four-dimensional vector space over GF(2).)
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Saturday, July 20, 2013
Monday, October 1, 2012
Foundation
» more
This, together with this morning's post involving the squares 16 and 9,
suggests a review of Conceit at Harvard (October 25, 2006), which
contains the following figure involving the squares 16, 9, and 25—
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Friday, August 2, 2024
For Olympic Dinghy Day (vide Google Doodle):
“Life’s Spiritual Dimension” — Templeton phrase
Templeton reportedly died on Saturday, May 16, 2015.
That date was also the release date for . . .
For a Templeton I actually respect , see a
Warren (PA) Times Observer obituary.
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“Life’s Spiritual Dimension” — Templeton phrase
“Life’s Spiritual Dimension” — Templeton phrase
Thursday, June 27, 2024
Die Berliner Mitschrift
https://page.math.tu-berlin.de/~felsner/Lehre/DSI11/Mitschrift-EH.pdf
The above S (3,4,8) is the foundation of the "happy family" of
subgroups of the Monster Group. See Griess and . . .
Related narrative and art —
"Battles argues that 'the experience of the physicality
of the book is strongest in large libraries,' and stand
among the glass cube at the center of the British Library,
the stacks upon stacks in Harvard’s Widener Library, or
the domed portico of the Library of Congress and tell me
any differently."
— Ed Simon, Binding the Ghost: Theology, Mystery, and
the Transcendence of Literature. Hardcover – April 19, 2022.
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Friday, May 31, 2024
Hex Ad: The Six-Pointed Star
For the star of the title, see "Levi-Strauss + Stella."
For a related hex, see an academic's weblog post from yesterday.
For an antidote to that hex, see a Wikipedia article . . .
Contrast the academic's phrase below with Wikipedia's "Pantocrator."
I prefer Yeats's (and Pantocrator's) Byzantium as a "soulful country."
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Wednesday, May 15, 2024
Passage for a Merry Minstrel: The Script Page*
"The bride hath paced into the hall,
Red as a rose is she;
Nodding their heads before her goes
The merry minstrelsy."
* The title is from the following passage . . .
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Monday, May 13, 2024
Wednesday, May 8, 2024
Art Grid: A Fulcrum for Pullman
"The bride hath paced into the hall,
Red as a rose is she;
Nodding their heads before her goes
The merry minstrelsy."
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Thursday, May 2, 2024
AI on Diamond Theory
The website PopAi.pro uses GPT-4 to summarize documents from the Web.
Input at PopAi on May 2, 2024:
The URL "http://www.log24.com/log/Diamond_Theory-1976-pp-1-12.pdf"
Output at PopAi, after a quick reading and analysis by GPT-4:
|
Diamond_Theory-1976-pp-1-12.pdf 12 Pages The document appears to be an excerpt from a preprint titled "Diamond Theory" by Steven H. Cullinane, dated 1976. The text discusses theoretical aspects of matrices composed of geometric figures, focusing on properties related to symmetry, permutations, and abstract structure. Main Concepts and Definitions: The author introduces the concept of a "geometric matrix," a matrix whose elements are geometric figures, specifically triangular subsets of a square. He defines a "diamond" as a foursquare matrix with triangular elements. The text details the remarkable properties of a diamond-like matrix D, including its symmetrical behavior under various permutations of elements, rows, columns, and sub-squares. Additionally, the text addresses the algebraic properties of matrices by relating their elements to those of a finite field. Theoretical Properties and Theorems: Several key theorems are proposed, demonstrating the structural properties of matrices. One fundamental theorem states that any matrix from a set F can be expressed as a linear combination of block matrices. Other theorems delve into the regularity of matrices, defining a matrix as "regular" if it remains unchanged or converts to its complement under certain flips and rotations. The text also describes the process of forming a "normal" matrix and the conditions under which matrices can be considered plaid or normal based on the behavior of their block maps and regularities. Applications and Miscellaneous Problems: The author reflects on the discovery of these properties during the process of creating an abstract painting and extends the exploration to include various types of matrices such as cyclic, quadratic, and skew foursquares. The document concludes with miscellaneous problems and an addendum on generalized matrix multiplication, suggesting further research directions and applications of the theory presented. In summary, "Diamond Theory" presents an intricate analysis of the structural and algebraic properties of matrices composed of geometric shapes, with implications for other mathematical domains. The work is a blend of geometry and abstract algebra, providing a foundation for understanding the symmetry and transformations of matrices with an artistic origin. Some questions you may ask: What properties of the diamond-like matrix D did the author discover in 1975? What is the relationship between the properties of D and the four group according to the document? How does the document define a 'good set' of four black and white geometric figures? What theorem is used to explain the behavior of superimposing two members of Mn(F) according to the document? |
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Tuesday, April 16, 2024
Tuesday, March 19, 2024
Monday, March 18, 2024
Monday, March 4, 2024
Report on the Diamond Theorem
by Google Gemini (Advanced)
|
by Google Gemini AI Monday, March 4, 2024
Absolutely! Here's an academic paper about the Cullinane diamond theorem. Please note that while I provide citations, in a fully formatted paper you'd need to adhere to your chosen academic style guide for proper formatting:
The Cullinane Diamond Theorem: Abstract This paper examines the Cullinane diamond theorem, a principle in finite projective geometry that offers unexpected insights into the symmetries found in graphic designs. The theorem, initially formulated by Steven H. Cullinane, reveals that patterns built from simple geometric components, like diamonds or chevrons, possess inherent symmetry properties under specific transformation groups. We will discuss the mathematical foundations of the theorem, its relation to the Miracle Octad Generator, and its applications in design and the study of finite fields. Introduction Symmetry plays a vital role in art and design, contributing to a sense of balance, harmony, and aesthetic appeal. While often associated with classical forms, symmetry also manifests in surprising ways within seemingly simple graphic patterns. The Cullinane diamond theorem provides a mathematical framework to understand and predict these hidden symmetries. Mathematical Background Finite Projective Geometries: The Cullinane diamond theorem has its roots in finite projective geometry. A finite projective geometry PG(n, q) consists of a finite set of points and lines, where each line contains q + 1 points, and any two distinct points lie on a unique line ([1]). Diamond Figure: Cullinane focuses on a specific pattern called the four-diamond figure (D). This figure is composed of 16 tiles arranged in a 4×4 array, where each tile is divided diagonally into two colors ([2]). Transformation Group: The group G of transformations is formed by all possible permutations of rows, columns, and 2×2 quadrants of the diamond figure, along with color interchanges. The size of this group is 322,560 ([2]). The Cullinane Diamond Theorem
Theorem:
Proof: Connections to the Miracle Octad Generator The Cullinane diamond theorem shares a relationship with R.T. Curtis's Miracle Octad Generator (MOG). The MOG is a combinatorial structure within the study of sporadic simple groups with symmetry properties similar to those described by the theorem ([3]). Applications Graphic Design: The theorem informs artistic compositions employing diamond and chevron-like shapes. Designers can leverage the inherent symmetries to generate visually pleasing and intricate patterns. Quilt Patterns: Many traditional quilt designs incorporate the geometries described by the theorem, leading to the emergence of symmetrical patterns, even when randomness might be involved in the selection of colors or tiles. Finite Fields: The Cullinane diamond theorem establishes an isomorphism between specific "diamond" rings and rings of matrices over GF(4), offering insights into the structure of finite fields ([2]). Conclusion The Cullinane diamond theorem elegantly connects abstract mathematics with the world of graphic design. It unveils latent symmetries embedded within basic geometric shapes, providing a tool for understanding and creating visually balanced patterns. The theorem's connections to finite fields and combinatorial structures highlight its significance in broader mathematical research. Citations [1] Weisstein, E. W. “Finite Projective Geometry.” From MathWorld–A Wolfram Web Resource. [invalid URL removed] [2] Cullinane, S. H. "Cullinane Diamond Theorem." Encyclopedia of Mathematics. https://encyclopediaofmath.org/wiki/Cullinane_diamond_theorem [3] Curtis, R. T. (1976). A New Combinatorial Approach to M₂₄. Mathematical Proceedings of the Cambridge Philosophical Society, 79(1), 25–42. doi:10.1017/S0305004100052075 Let me know if you'd like me to expand on any particular aspect or provide additional citations!
1. www.hellenicaworld.com/Science/Mathematics/en/MathieuGroup.html
|
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by Google Gemini (Advanced)
by Google Gemini (Advanced)
Monday, February 19, 2024
Fulcrum
From Log24 on September 19, 2023 —
Adapted image —
Related reading —
Related art — Square Round and Round Square.
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Saturday, November 25, 2023
Phrases by Archimedes —
“A Place to Stand” and “The Sand Reckoner”
"The hard sand breaks,
And the grains of it
Are clear as wine."
— By "H. D."… “Hermes of the Ways,”
Pp. 21-23, Vol. 1, No. 5 of The Glebe —
Des Imagistes , February, 1914.
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“A Place to Stand” and “The Sand Reckoner”
“A Place to Stand” and “The Sand Reckoner”
Wednesday, October 25, 2023
House Call
"When you build your house
Then call me home"
— Fleetwood Mac, "Sara"
“If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Sunday, October 1, 2023
The Usual Suspects: Schmeikal
From a search in this journal for "Schmeikal" —
|
Schmeikal Bio https://keplerspaceinstitute.com/project/volume-9-number-1/ [Spring 2020] [Page 7] — Introduction by the Editors We have been blessed throughout the publication history of the Journal of Space Philosophy, beginning in 2012, with the volunteer service of 42 professionals in the Space community to act as reviewers and consultants to our authors. They have been listed in the final article of each published issue. We are proud to announce with this letter the addition of our latest Senior Consultant, Dr. Bernd Anton Schmeikal. [Image of Dr. Schmeikal] This Letter to the Editor is about Dr. Schmeikal. Bernd Anton Schmeikal, born May 15, 1946, is a retired freelancer in research and development, qualified in Sociology with a treatise about cultural time reversal. He is a real maverick, still believing that social life can be based on openness and honesty. As a PhD philosopher from Vienna, with a typical mathematical physics background, he entered the Trace Analysis Group of the UA1 Experiment at CERN, under the leadership of Walter Thirring, in 1965. This was in the foundation phase of the Institute for High Energy Physics (HEPhy) at the Austrian Academy of Science. He has always been busy solving fundamental problems concerning the unity of matter and space-time, the origin of the HEPhy standard model, and the phenomenology of relativistic quantum mechanics. In the Sociology Department of the Institute for Advanced Studies (IHS Vienna), he helped James Samuel Coleman to conceive his mathematics of collective action as a cybernetic system, and he gave the process of internalization of 7 ………………. End of page 7 [Page 8] — Journal of Space Philosophy 9, No. 1 (Spring 2020) collective values an exact shape. He implemented many transdisciplinary research projects for governmental and non-governmental organizations, universities, and non-university institutions, and several times he introduced new views and methods. He founded an international work stream that, for the first time, worked under the name of the Biofield Laboratory (BILAB). Although close to fringe science and electromedicine, the work of BILAB had a considerable similarity to the Biological Computer Laboratory run earlier by Heinz von Foerster. Lately, he has applied Foerster’s idea of a universal relevance of hyperbolic distributions (Zipf’s law) in social science to the labor market. This signifies a last contribution to the research program of the Wiener Institute for Social Science Documentation and Methodology (WISDOM) under the sponsorship of the Austrian Federal Presidential Candidate Rudolf Hundstorfer. Dr. Schmeikal is convinced that a unity of science and culture can be achieved, but that this demands more than one Einstein. Consequently, he sought cooperation with Louis Kauffman and Joel Isaacson. Dr. Bernd Schmeikal’s review and evaluation of Joel Isaacson and Louis Kauffman’s Recursive Distinctioning (aka “Nature’s Cosmic Intelligence”) research and papers, published in the first issue of the JSP, Fall 2012, again in the Special JSP Issue on Recursive Distinctioning, Spring 2016, and again in the Fall 2017 issue, are very valuable contributions to this forefront science investigation of Nature’s Cosmic Intelligence. Dr. Schmeikal, University of Vienna Professor in mathematics, linguistics, and physics is one of the world’s distinguished scholars for this special field of universe autonomous intelligence. He begins his abstract with the statement: “This paper investigates a universal creative system,” and ends it with “That is to say, our universe may be a representation of Isaacson’s system, and entertainingly, with his US Patent specification 4,286,330, 1981, it seems he has patented creation.” Reports on the four annual KSI-sponsored Conferences for Recursive Distinctioning, to date, can be found in JSP publications. Dr. Schmeikal’s latest book publication is Nuclear Time Travel and the Alien Mind, published by Nova Science Publishers, New York. In 119 pages, Dr. Schmeikal tells the historic story of unidentified objects, and the knowns and unknowns of advanced space-time warping time-travel technology. He includes a September 24, 1947 top secret letter of President Harry Truman to Secretary of Defense Forrestal, authorizing research into these matters, but confining ultimate disposition to be solely under the Office of the President. Dr. Schmeikal’s discussions of the impacts of the extraterrestrial mind on past Earth events give a research variable as we attempt to understand and predict future outcomes of attempts at improving humanity’s prospects (see Yehezkel Dror, JSP, Summer 2015 and Kepler Space Institute, book publication, 2019) as we humans proceed with exploring, developing and building human Space settlements. Bob Krone and Gordon Arthur Founding and Current Editors, Journal of Space Philosophy April 15, 2020 8 …………………………… [End of page 8] |
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Tuesday, September 26, 2023
Former-Day Saint
"Birthday, death-day — what day is not both?" — Updike
The actor who played "Illya Kuryakin" reportedly died yesterday —
" David Keith McCallum Jr. was born on Sept. 19, 1933, into
a musical family in Glasgow. His father was the first violinist
for the Royal Philharmonic Orchestra in London; his mother,
Dorothy Dorman, was a cellist. He would later tell interviewers
that his Scotch Presbyterian upbringing had left him emotionally
circumscribed.
'We Scots, we tend to be awfully tight inside,' he told TV Guide
in 1965. 'It has hurt me as an actor to be so — so naturally restricted.' "
— Leslie Kaufman in The New York Times
This journal on McCallum's 90th birthday — Sept. 19, 2023 —
"You take the high road and . . . ."
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Monday, July 31, 2023
Thursday, July 20, 2023
Wednesday, July 19, 2023
Sunday, July 9, 2023
Art of the Steal
The Wikipedia article on Christoper Knight, the LA Times art critic
in tonight's previous post, leads to . . .
See as well Barnes in this journal.
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Thursday, June 15, 2023
Michaelmas 2019
Transcribed from a PDF:
|
Received September 29, 2019, accepted October 15, 2019, Digital Object Identifier 10.1109/ACCESS.2019.2949310
A Method for Determining
ZIYU WANG1 , XIAO ZENG1 , JINZHAO WU2,3, AND
1Big Data Research Center, School of Computer Science
2Guangxi Key Laboratory of Hybrid Computation and
3School of Computer and Electronic Information,
Corresponding authors:
This work was supported in part by the National Natural Science Foundation
ABSTRACT
INDEX TERMS Logic synthesis, Boolean functions, |
Meanwhile . . .
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Tuesday, May 9, 2023
The Blacklist School
The most recent "Blacklist" episode suggests a review —
"Where past and future are gathered" — Four Quartets
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Wednesday, May 3, 2023
Kernels
Continued from yesterday's "Kernel" —
The ACM (Association for Computing Machinery)
has a news release today on an expert on "kernels,"
in the sense that they are used in AI —
"Schölkopf [link added] is recognized for his
widely used research in machine learning,
advancing both mathematical foundations and
a broad range of applications in science and
industry."
From Schölkopf in 2002 —
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Friday, March 24, 2023
Law in Becoming, Play in Necessity — Nietzsche
(See Nietzsche references in this journal.)
|
March 24, 2023 08:00 PM SANTA CLARA, Calif. — (BUSINESS WIRE) — Intel and the Gordon and Betty Moore Foundation announced today that company co-founder Gordon Moore has passed away at the age of 94. The foundation reported he died peacefully on Friday, March 24, 2023, surrounded by family at his home in Hawaii. (Moore link added.) |
Related surrealistic robot drama from The New York Times —
Bad Cinderella and the Orgy Dome Cleanup Crew
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Wednesday, December 28, 2022
The Santa Fe Institute as Magisterium Wannabe
"The novelist Cormac McCarthy has been a fixture around
the Santa Fe Institute since its embryonic stages in the
early 1980s. Cormac received a MacArthur Award in 1981
and met one of the members of the board of the MacArthur
Foundation, Murray Gell-Mann, who had won the Nobel Prize
in physics in 1969. Cormac and Murray discovered that they
shared a keen interest in just about everything under the sun
and became fast friends. When Murray helped to found the
Santa Fe Institute in 1984, he brought Cormac along, knowing
that everyone would benefit from this cross-disciplinary
collaboration." — https://www.santafe.edu/news-center/news/
cormac-and-sfi-abiding-friendship
Joy Williams, review of two recent Cormac McCarthy novels —
"McCarthy has pocketed his own liturgical, ecstatic style
as one would a coin, a ring, a key, in the service of a more
demanding and heartless inquiry through mathematics and
physics into the immateriality, the indeterminacy, of reality."
A Demanding and Heartless Coin, Ring, and Key:
COIN
RING
"We can define sums and products so that the G-images of D generate
an ideal (1024 patterns characterized by all horizontal or vertical "cuts"
being uninterrupted) of a ring of 4096 symmetric patterns. There is an
infinite family of such 'diamond' rings, isomorphic to rings of matrices
over GF(4)."
KEY
"It must be remarked that these 8 heptads are the key to an elegant proof…."
— Philippe Cara, "RWPRI Geometries for the Alternating Group A8," in
Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference
(July 16-21, 2000), Kluwer Academic Publishers, 2001, ed. Aart Blokhuis,
James W. P. Hirschfeld, Dieter Jungnickel, and Joseph A. Thas, pp. 61-97.
For those who prefer a "liturgical, ecstatic style" —
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Thursday, November 24, 2022
The Drum Machine
"A struggling music producer sells his soul to a 1970s drum machine."
— Summary of a short film by Kevin Ignatius, "Hook Man."
The music producer pawns his current drum device
and acquires a demonic 1970s machine.
Artistic symbolism —
The 16-pad device at left may be viewed by enthusiasts of ekphrasis
as a Galois tesseract, and the machine at right as the voice of
Hal Foster, an art theorist who graduated from Princeton in 1977.
For an example of Foster's prose style, see
the current London Review of Books.
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Friday, November 18, 2022
Bullshit Studies: Cohen on Kiefer
" La Ribaute is hard to classify. It is now controlled by
a foundation for which Kiefer chose the name 'Eschaton,'
meaning the final event in the divine plan, or the end of
the world. 'You can say it’s the end of the beginning,'
Kiefer said. 'Eschaton means that something comes after.'
So why, I asked, did he pick this name? 'Because it’s the
beginning.' "
I prefer T. S. Eliot on ends and beginnings, as well as
R. A. Wilson on the Eschaton.
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Saturday, September 24, 2022
Nine and Sixteen: In Search of Common Ground
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Tuesday, July 12, 2022
“Tell it Skewb” continues.
Previously on Log24:
"Tell it Skewb." — Motto adapted from Emily Dickinson.
On further investigation . . .
From the above Sanfilippo date —
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Object Lesson: The Quelling
"The successful artist shares with the politician
a recurrent temptation to indulge in emotional claptrap.
Bernard Bosanquet in Three Lectures on Aesthetic (1915)
proposed that this urge to chase after tears or laughter
could be quelled by attaching the art-emotion to a particular object
and not a set of reactions. His consequent definition of art was
'feeling expressed for expression’s sake.' Notice, however, that
this is something only the deranged would dream of wanting in
real life. Our everyday expressions of feeling are spontaneous and
practical; they are never 'for expression’s sake.' By contrast,
aesthetic feeling is self-sufficient."
— David Bromwich in The Nation, July 11, 2022
A Particular Object —
"Tell it Skewb." — Motto adapted from Emily Dickinson.
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Tuesday, June 7, 2022
A Square for the Circle
The new URL matrix.bingo forwards to
http://m759.net/wordpress/?s=5×5 .
“If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Friday, May 6, 2022
Use Your Noodle (For Byron Gogol*)
An essay from . . .
The Shape of Things: A Philosophy of Design Wittgenstein’s Architecture The universe of texts can be seen as a landscape. In it one can make out mountains and valleys, rivers and lakes, castles, farmyards and inner-city slums. On the horizon of the scene visualized in this way, the Bible and Homer appear as gigantic ice-covered mountains. The vast, tranquil lake of Aristotle’s texts, where fishermen idly throw their nets and philologists row their boats, occupies a part of the valley bottom. There, the tumbling waterfall of Nietzsche is captured by the broad river of modern pragmatism. Towering above everything, the Gothic cathedral of St Thomas Aquinas’s Summae dominates the cathedral square of the city, in which the roofs and gables of Baroque speculations jostle one another. In the suburbs of this city, one catches sight of the Romantic, Realist and Modernist housing-blocks and factories of more recent litera¬ ture; somewhat apart from all these stands a small, apparently insignificant house resembling scaffolding more than a finished building: Wittgenstein’s building. This little house is called the Tractatus. This name isn’t the product of a one-track mind. For when one enters the house, one notices immediately that this is not a place that has lost track of things. Quite the opposite: It is a place of mirror- images. The house stands on six foundation pillars which support one another by means of cross-beams organized in a hierarchy. In the middle, however, there rises a seventh pillar whose function it is to cut through the building and free it from the ground. So the house with all its corners, angles and joints is protected, armoured and impregnable. And yet, and for that very reason, it is threatened with collapse and disappearance without trace – condemned in advance and from the outset. The building is set out: It consists of propositions. Every proposition presupposes all the preceding ones and is itself the 76 presupposition of all the following propositions. Proposition by proposition, anyone who enters progresses through the prescribed rooms, and his step is supported by consistencies. Suddenly, with one proposition, one single proposition, the ground gives way beneath his feet. He falls head first into the abyss. Wittgenstein’s house is situated in a suburb of that city whose cathedral square is dominated by the towers of Thomas Aquinas’s cathedral. The small, modest pillars of Wittgenstein’s house support one another according to the same logico- philosophical method as the pillars of the cathedral support one another. But there appears to be a world of difference between the cathedral and the little house: The cathedral is a ship pointing in the direction of heaven, and the little house is a trap-door pointing in the direction of a bottomless abyss. But be careful: May Thomas Aquinas not have been right in saying after his revelation that everything he had written before was like straw? May not the heaven above the cathedral be the same black hole as the abyss beneath the little house? May not Wittgenstein’s little house be the cathedral of today? And those mirrors whose images simultaneously mirror one another, may they not be our equivalent of stained-glass windows? The landscape portrayed in this essay, it goes without saying, is a metaphor. Is it possible to identify it as Vienna? And is it possible for anyone entering Wittgenstein’s little house in that unlikely place to make out a hint of the unsayable? What we cannot speak about we must pass over in silence. 77 |
Click the above image to enlarge.
See as well . . .
Update of 2:40 AM May 7, 2022 —
Flusser's seven "pillars" appear to be the main sections of the Tractatus
— numbered 1 through 7, with many intermediate numbered passages.
For a more geometric meditation on "the shape of things," see other
posts tagged "Shape Constant" in this journal.
*Byron Gogol is a tech magnate in the HBO series "Made for Love."
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Monday, May 2, 2022
Overarching Rhetoric
" While quantum theory has proven to be supremely successful
since its development a century ago, physicists have struggled to
unify it with gravity to create one overarching ‘theory of everything.’ "
— News release 1-May-2022 from
Foundational Ouestions Institute, FQXi
See as well the new URL "overarching.group."
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Wednesday, April 27, 2022
Sunday, February 6, 2022
Animating the Savoir
". . . It is as if
We had come to an end of the imagination,
Inanimate in an inert savoir.”
— Wallace Stevens, “The Plain Sense of Things”
"In my end . . . ." — T. S. Eliot
|
Thursday, March 22, 2018
The Diamond Cube
|
See a note from Sept. 15, 1984
(perhaps the last day of life for Richard Brautigan).
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Saturday, January 29, 2022
As If
Continued from this journal's posts of March 1, 2021 —
As If
|
"Time past and time future . . ." — T. S. Eliot
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Friday, July 30, 2021
The Secret Subterranean River
The "secret, subterranean river" of Shulevitz is
a flow of thought favorable to the cause of feminism,
but not necessarily to other "revolutionary" ideas.
Compare and contrast:
"Where Alph, the sacred river, ran"
— Coleridge, Kubla Khan
"Where Aleph the sacred symbol ran"
— Cullinane, "The Coxeter Aleph"
For group discussion:
How (if at all) is the "finitude" of Heidegger related to
mathematical finitude and The King of Infinite Space ?
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Saturday, July 10, 2021
Plan 9 from Ancient China
.jpg)
Robert A. Wilson on symmetries of the ninefold square —
|
"All of these ideas have shown promise at some time or other, and some are still under active investigation. But my conclusion after all this work is that the part of algebra that shows the most promise for genuinely useful applications to fundamental physics is the representation theory, real, complex, integral and modular, of the group GL(2, 3). There is, of course, no guarantee that a viable theory can be built on this foundation. But it appears to be the only part of algebra that both has a reasonable chance of success and has not already been exhaustively explored in the physics literature. It is therefore worth serious consideration." — "Potential applications of modular representation theory to quantum mechanics," arXiv, May 28, 2021, revised June 7, 2021. |
See as well GL(2,3) in this journal .
Related material: Christmas Eve 2012.
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Monday, July 5, 2021
For Stonehearst Asylum
Robert A. Wilson on symmetries of the ninefold square —
|
"All of these ideas have shown promise at some time or other, and some are still under active investigation. But my conclusion after all this work is that the part of algebra that shows the most promise for genuinely useful applications to fundamental physics is the representation theory, real, complex, integral and modular, of the group GL(2, 3). There is, of course, no guarantee that a viable theory can be built on this foundation. But it appears to be the only part of algebra that both has a reasonable chance of success and has not already been exhaustively explored in the physics literature. It is therefore worth serious consideration." — "Potential applications of modular representation theory to quantum mechanics," arXiv, May 28, 2021, revised June 7, 2021. |
See as well GL(2,3) in this journal .
Some may consider more relevant the remarks of a different Robert A. Wilson —
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Monday, June 21, 2021
The Bauhaus Dance
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Thursday, June 3, 2021
Notes towards the Redefinition of Culture
"My little horse must think it queer" — Robert Frost.
This is from a poem mentioned here on December 22, 2004,
in a post titled "The Longest Night."
Related material from December 21, 2004 —
And then there is the Timeless Square . . .
See "Framed" (May 30) and "In Memory of Ernst Eduard Kummer" (May 14).
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Monday, April 26, 2021
A Memoir of Her Time
Alex Traub in today’s online New York Times —
“Helen Weaver, who fell in love with Jack Kerouac months before
‘On the Road’ rocketed him into the literary stratosphere, and who
53 years later made a record of their romance in an enduring book
of her own, died on April 13 at her home in Woodstock, N.Y.
She was 89.”
“The Beat rebel charmed Ms. Weaver with gentleness.
He agreed to attend a dinner party with Ms. Weaver’s
parents in New Milford, Conn., and began the evening
by asking whether they believed in God.”
“Helen Hemenway Weaver was born on June 18, 1931,
in Madison, Wis. Her father, Warren, was chairman of
the mathematics department at the University of
Wisconsin, and her mother, Mary (Hemenway) Weaver,
was a schoolteacher and later a homemaker.
Helen grew up in Scarsdale, N.Y., where the family had
moved when her father began working as an executive at
the Rockefeller Foundation and other nonprofit organizations.”
In Nomine Patris
The Times‘s Warren link above leads to an obituary of Warren Weaver:
|
He was the author, or co‐author, of books ranging from works on pure science during his early career to “Lady Luck,” a popular discussion of the theory of probability that sold widely in paperback. Wrote About ‘Alice’ Among his other books was “Alice in Many Tongues,” which dealt with foreign translations of “Alice in Wonderland.” He had the largest collection of the writing of Lewis Carroll, the author of “Alice,” now owned by the University of Texas. |
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Thursday, March 4, 2021
Continuity
Actually, Dirac “bridged math and physics” much earlier —
“Spinors, which are a kind of square root of vectors, had been introduced
in algebra and also in physics as part of Paul Dirac’s theory of the electron.
A spin structure on a manifold allows such square roots to exist.”
— Quanta Magazine today, article by Daniel S. Freed
See The Eddington Song and . . .
Poetic paraphrase —
“How can we tell the singer from the song?”
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Monday, March 1, 2021
As If
" . . . It is as if
We had come to an end of the imagination,
Inanimate in an inert savoir."
— Wallace Stevens, "The Plain Sense of Things"
For such a savoir, see Cube School.
See as well the Stevens online concordance.
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Thursday, December 3, 2020
Bunker Bingo
See as well 5×5, The Matrix of Abraham, and Deutsche Schule Montevideo .
“If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Tuesday, November 24, 2020
Sunday, November 1, 2020
Art Theory
“If you have built castles in the air, your work need not be lost;
that is where they should be. Now put the foundations under them.”
— Henry David Thoreau
Between, or: Interality Illustrated (according to Sherald)
“We live in between the lines;
in between the cracks . . . .
That’s where the bonds are formed. ”
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Sunday, September 13, 2020
Braving the Elements
The title is that of a book of poems by James Merrill
that includes “The Emerald.”
“As above, so below.” — The Emerald Tablet
“The Emerald Tablet … is a compact and cryptic piece of
the Hermetica reputed to contain the secret of the prima materia
and its transmutation. It was highly regarded by European alchemists
as the foundation of their art and its Hermetic tradition.” — Wikipedia
Animated version of Book I, Proposition 47, Euclid’s Elements —
|
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Friday, September 11, 2020
In Memoriam
|
From the Vanderbilt University obituary of Vaughan F. R. Jones —
"During the mid-1980s, while Jones was working on a problem in von Neumann algebra theory, which is related to the foundations of quantum mechanics, he discovered an unexpected link between that theory and knot theory, a mathematical field dating back to the 19th century. Specifically, he found a new mathematical expression—now known as the Jones polynomial—for distinguishing between different types of knots as well as links in three-dimensional space. Jones’ discovery had been missed by topologists during the previous 60 years, and his finding contributed to his selection as a Fields Medalist.
'Now there is an area of mathematics called said Dietmar Bisch, professor of mathematics." [Link added.] |
Related to Jones's work —
"Topological Quantum Information Theory" at
the website of Louis H. Kauffman —
http://homepages.math.uic.edu/~kauffman/Quanta.pdf.
Kauffman —
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Wednesday, August 5, 2020
Rendezvous with Drama
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Wednesday, April 22, 2020
One with Everything
The title is of course from an old joke about mystic philosophies.
Related remarks by John Archibald Wheeler —
“Remarkable issues connected with the puzzle of existence
confront us today in Hermann Weyl’s domain of thought.
Four among them I bring before you here as especially interesting:
(1) What is the machinery of existence?
(2) What is deeper foundation of the quantum principle?
(3) What is the proper position to take about the existence of
the “continuum” of the natural numbers? And
(4) What can we do to understand time as an entity, not precise and
supplied free of charge from outside physics, but approximate and
yet to be derived from within a new and deeper time-free physics?
In brief, how come time?
What about the continuum?
How come the quantum?
What is existence?”
— John A. Wheeler, “Hermann Weyl and the Unity of Knowledge,”
American Scientist 74, no. 4 (1986): 366–75. Reprinted in
John A. Wheeler, At Home in the Universe
(American Institute of Physics, December 1, 1995).
The above bibliographic data is from . . .
Schrank, Jeffrey. Inventing Reality: Stories We Create To Explain Everything .
Gatekeeper Press. Kindle Edition, March 14, 2020.
For further scholarly details, see a version at JSTOR:
“…the article is adapted from the concluding address given at
the Hermann Weyl Centenary Congress, University of Kiel, 3 July 1985.”
— https://www.jstor.org/stable/27854250.
I prefer Charles Williams on “the Unity of Knowledge.”
See the 15 instances of the phrase “the Unity” in his 1931 novel Many Dimensions .
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Sunday, April 5, 2020
Saturday, January 11, 2020
Mathematics or Theology?
Hersh wrote a paper with a title containing the phrase
“The Kingdom of Math is Within You.”
In his memory, see Log24 posts from the date of his death
tagged Inner-Space Variations.
Related literature: Hersh's "Death and Mathematics Poems."
See as well this journal on the above publication date.
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Wednesday, November 6, 2019
Soul Snatchers
From All Souls' Day 2015 —
Related entertainment —
Invasion of the Soul Snatchers (Wild Palms review, 1993).
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Sunday, September 15, 2019
For Weisheit, the Rabbi
See also Log24 remarks from the date of Greene's death
in posts now tagged Bregnans.
A page related to Eleanor Cook's "wonderful first line"
quoted above from A Reader's Guide to Wallace Stevens :
A Reader's Guide to Eleanor Cook —
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Monday, September 9, 2019
The Montenegro Contingency
(For Harlan Kane)
"While digging in the grounds for the new foundation,
the broken fragments of a marble statue were unearthed."
— From Thomas Hardy, "Barbara of the House of Grebe,"
quoted in an epigraph to Paul de Man's "Shelley Disfigured,"
in turn quoted by Barbara Johnson on page 231 of Persons
and Things (Harvard paperback, 2010).
From "the world of the unintentional, the contingent, the minute,
and the particular" (Kovacevic, U. of Montenegro, 2011) —
Yes, we received your payment. No, it wasn't late, but it was for $78.13, and the bill was for $78.31. Okay, great. Read more: https://www.springfieldspringfield.co.uk/ movie_script.php?movie=the-circle
Another such transposition: Pages 213 and 231 in a search
for "gaps" in a 2010 paperback discussion of Lacan —
These pages are as follows —
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Tuesday, August 20, 2019
Ice Giants and Fire Gods: Mind the Gap
From my reading Monday morning —
From the online New York Times this afternoon —
Related literature —
For the Church of Synchronology —
The Gigantomachia page above is dated September 20, 2003.
See as well my own webpage from that date: "The Form, the Pattern."
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Monday, July 1, 2019
“The Ontological Secret”
The phrase "ontological secret" is from 1927 —
" Beauty is thus 'a flashing of intelligence…
on a matter intelligibly arranged' or, as Maritain
adds in the 1927 edition of Art and Scholasticism ,
it is 'the ontological secret that [things] bear within
them[selves], their spiritual being, their operating
mystery.' "
— John G. Trapani, Jr., "'Radiance': The Metaphysical Foundations
of Maritain's Aesthetics," pp. 11-19 in Beauty, Art, and the Polis ,
ed. by Alice Ramos, publ. by American Maritain Association, 2000.
This 1927 phrase may be the source of McLuhan's 1944
"ontological secret" —
From a search in this journal for "Object of Beauty" —
“She never looked up while her mind rotated the facts,
trying to see them from all sides, trying to piece them
together into theory. All she could think was that she
was flunking an IQ test.”
— Steve Martin, An Object of Beauty
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Sunday, May 19, 2019
The Building Blocks of Geometry
From "On the life and scientific work of Gino Fano"
by Alberto Collino, Alberto Conte, and Alessandro Verra,
ICCM Notices , July 2014, Vol. 2 No. 1, pp. 43-57 —
|
" Indeed, about the Italian debate on foundations of Geometry, it is not rare to read comments in the same spirit of the following one, due to Jeremy Gray13. He is essentially reporting Hans Freudenthal’s point of view: ' When the distinguished mathematician and historian of mathematics Hans Freudenthal analysed Hilbert’s Grundlagen he argued that the link between reality and geometry appears to be severed for the first time in Hilbert’s work. However, he discovered that Hilbert had been preceded by the Italian mathematician Gino Fano in 1892. . . .' " 13 J. Gray, "The Foundations of Projective Geometry in Italy," Chapter 24 (pp. 269–279) in his book Worlds Out of Nothing , Springer (2010). |
Restoring the severed link —
See also Espacement and The Thing and I.
Related material —
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Tuesday, May 14, 2019
Change
"Is there no change of death in paradise?" — Wallace Stevens
From a New Yorker book review dated May 13 —
"In 'Field Flowers,' Glück’s flower scoffs that 'absence of change'
is humanity’s 'poor idea of heaven.' But the religious believer
might object that Hägglund’s idea of eternity is equally poor."
Here James Wood is reviewing Martin Hägglund’s
This Life: Secular Faith and Spiritual Freedom
(Pantheon, March 5, 2019).
See also posts tagged Change Arises in this journal.
Hägglund himself appeared here on June 21, 2014.
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Tuesday, April 23, 2019
Tree
A check of an author cited in the previous post yields —
The cover illustration above is by Kay Nielsen . . .
"FROM 'EAST OF THE SUN AND WEST OF THE MOON'
('AND FLITTED AWAY AS FAR AS THEY COULD … '), 1914."
(Paris Review , December 3, 2015.)
See as well the April 1977 poem "Winter Tree" by Jon Lang and . . .
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Sunday, March 17, 2019
Just Another Block in the Wall
Yesterday's post Grundlagen —
Midrash on yesterday's Grundlagen —
A poem linked to here on the above "building blocks" date, in the
Log24 post Sermon of 11 AM ET Sunday, 15 September 2013 —
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Wednesday, January 16, 2019
Permutahedron Dream
The geometric object of the title appears in a post mentioning Bourgain
in this journal. Bourgain appears also in today's online New York Times —
https://www.nytimes.com/2019/01/16/
obituaries/jean-bourgain-dead.html .
Bourgain reportedly died on December 22.
An image from this journal on that date —
Related poetic meditations —
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Wednesday, January 9, 2019
Desperately Seeking Clarity*
A much earlier, much truer, obituary —
* A sequel to Resonant Clarity and Desperately Seeking Resonance.
Quantum electrodynamics is also known as QED.
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Monday, December 31, 2018
Eve’s Riddle
The Dickinson poem quoted above is numbered 373 at
the Poetry Foundation.
See also Eternity + 373 in this journal.
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Saturday, December 29, 2018
Winter Tree
The title is that of a 1977 poem by Jon Lang.
A different sort of narrative tree, from The Onion on the
date Friday, July 1, 2016, was illustrated in the previous post.
Material from this journal related to July 1, 2016,
and the following day, a Saturday, is now tagged
"Saturday Night in the Labyrinth."
"A Damned Serious Business." — Rex Harrison on comedy
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Friday, December 28, 2018
Phenomenology of Viewing
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Saturday, December 22, 2018
The Hat Tip
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Thursday, November 8, 2018
Reality vs. Axiomatic Thinking
From https://blogs.scientificamerican.com/…
|
A Few of My Favorite Spaces:
The intuition-challenging Fano plane may be By Evelyn Lamb on October 24, 2015
"…finite projective planes seem like |
For Fano's axiomatic approach, see the Nov. 3 Log24 post
"Foundations of Geometry."
For the Fano plane's basis in reality , see the eightfold cube
at finitegeometry.org/sc/ and in this journal.
See as well "Two Views of Finite Space" (in this journal on the date
of Lamb's remarks — Oct. 24, 2015).
Some context: Gödel's Platonic realism vs. Hilbert's axiomatics
in remarks by Manuel Alfonseca on June 7, 2018. (See too remarks
in this journal on that date, in posts tagged "Road to Hell.")
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Wednesday, November 7, 2018
Defense Against the Dark Arts
"What is the Necropastoral?" was published on April 29th, 2014.
Also on April 29th, 2014 —
See as well Christianity and Culture by T. S. Eliot.
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Friday, November 2, 2018
Elevation of the Hostess
Or: Netflix and Chill on All Souls' Day
Midrash from Huffington Post (click to enlarge) —
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Wednesday, July 11, 2018
Plato and Paradigms, Revisited
"Plato thought nature but a spume that plays
Upon a ghostly paradigm of things"
— W. B. Yeats, "Among School Children"
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Friday, October 13, 2017
Speak, Memra
The above was suggested by a Log24 review of October 13, 2002,
which in turn suggested a Log24 search for Carousel that yielded
(from Bloomsday Lottery) —
See as well Asimov's "prime radiant," and an illustration
of the number 13 as a radiant prime …
"The Prime Radiant can be adjusted to your mind,
and all corrections and additions can be made
through mental rapport. There will be nothing to
indicate that the correction or addition is yours.
In all the history of the Plan there has been no
personalization. It is rather a creation of all of us
together. Do you understand?"
"Yes, Speaker!"
— Isaac Asimov,
Second Foundation , Ch. 8: Seldon's Plan
"Before time began, there was the Cube."
— Optimus Prime
See also Transformers in this journal.
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Monday, October 9, 2017
Saturday, September 30, 2017
Paradoxes for Oxymorons
"This poem is concerned with language on a very plain level."
— "Paradoxes and Oxymorons" by John Ashbery,
quoted here in the post Take Your Pick of Dec. 16, 2011.
"The problem is a paradox of the veridical type,
because the correct result (you should switch doors)
is so counterintuitive it can seem absurd,
but is nevertheless demonstrably true."
— Wikipedia on the Monty Hall problem.
Related material —
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Saturday, July 29, 2017
MSRI Program
"The field of geometric group theory emerged from Gromov’s insight
that even mathematical objects such as groups, which are defined
completely in algebraic terms, can be profitably viewed as geometric
objects and studied with geometric techniques."
— Mathematical Sciences Research Institute, 2016:
See also some writings of Gromov from 2015-16:
- Memorandum Ergo (October 29, 2015)
- Great Circle of Mysteries (November 15, 2015)
- Quotations and Ideas (April 15, 2016)
For a simpler example than those discussed at MSRI
of both algebraic and geometric techniques applied to
the same group, see a post of May 19, 2017,
"From Algebra to Geometry." That post reviews
an earlier illustration —
For greater depth, see "Eightfold Cube" in this journal.
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Wednesday, July 12, 2017
Friday, July 7, 2017
Psycho History
The title was suggested by the term “psychohistory” in
the Foundation novels of Isaac Asimov. See the previous post.
See also a 2010 New York Times review of
DeLillo’s novel Point Omega . The review is titled,
without any other reference to L’Engle’s classic tale
of the same name, “A Wrinkle in Time.”
Related material: The Crosswicks Curse.
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A Prime Radiant for Krugman
Paul Krugman:
Asimov’s Foundation novels grounded my economics
In the Foundation novels of Isaac Asimov …
“The Prime Radiant can be adjusted to your mind, and all
corrections and additions can be made through mental rapport.
There will be nothing to indicate that the correction or addition
is yours. In all the history of the Plan there has been no
personalization. It is rather a creation of all of us together.
Do you understand?”
“Yes, Speaker!”
— Isaac Asimov, Second Foundation , Ch. 8: Seldon’s Plan
“Before time began, there was the Cube.“
See also Transformers in this journal.
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Wednesday, June 7, 2017
Anywhere in Years
" In 1965, Mr. Simmons, an incisive, erudite reviewer and essayist,
won a William Faulkner Foundation Award for Powdered Eggs [ 1964 ],
recognized as a notable first novel. (He wryly called it his
'64th first novel.') The Boston Globe said it was 'certainly among
the outstanding fictions of the ′60s.' [ Later, in 1971,* ] The novelist
Harry Crews heralded him as 'one of the finest comic voices to appear
anywhere in years.' "
— Sam Roberts in a New York Times obituary this evening
See also Harry Crews in this journal.
Roberts says Simmons also wrote "a savage sendup of The New York Times
Book Review , where he had worked as an editor for three decades."
Some not-so-savage related material —
* "Anywhere in years" — From http://www.nytimes.com/1971/11/21/archives/
an-oldfashioned-darling-by-charles-simmons- 202-pp-new-york-coward.html
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Wednesday, January 18, 2017
An Associative Function …
Quoted here on December 16, 2006 —
See also …
-
"Ryan Reynolds Named Hasty Pudding’s
2017 Man of the Year" -
Reviews of Reynolds' 2015 film "Self/Less" and of
the earlier similar film "Seconds" —4 July 2015 9:00 AM, PDT | The Wrap |
"Ben Kingsley plays a New York real estate mogul who
pays big bucks to have his consciousness microwaved
into Ryan Reynolds' body in 'Self/less,' but the real
reheating of leftovers has already occurred: this new
science-fiction thriller borrows the foundation of a much
better film — John Frankenheimer’s 1966 'Seconds' —
and strips it of any larger meaning."
The date of the "Seconds" review above, 16 Dec. 2006, was
the reason for the requotation in the first paragraph above.
Comments Off on An Associative Function …
Sunday, December 4, 2016
London Recessional
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Sunday, November 13, 2016
Dinkey
Sewell is supposedly modeled on literary critic R. P. Blackmur.
For a quotation from Blackmur, see a post of June 1, 2006.
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Friday, October 7, 2016
Paz
The Paz quote below is from the last chapter
of his book, titled "The Dialectic of Solitude."
The phrase "dialectic of solitude" has been applied also to a 1967
book by the Colombian writer Gabriel García Márquez:
|
The conclusion of One Hundred Years of Solitude , "He was so absorbed that he did not feel the second surge of wind either as its cyclonic strength tore the doors and windows off their hinges, pulled off the roof of the east wing, and uprooted the foundations. Only then did he discover that Amaranta Úrsula was not his sister but his aunt, and that Sir Francis Drake had attacked Riohacha only so that they could seek each other through the most intricate labyrinths of blood until they would engender the mythological animal that was to bring the line to an end. Macondo was already a fearful whirlwind of dust and rubble being spun about by the wrath of the biblical hurricane when Aureliano skipped eleven pages so as not to lose time with facts he knew only too well, and he began to decipher the instant that he was living, deciphering it as he lived it, prophesying himself in the act of deciphering the last page of the parchments, as if he were looking into a speaking mirror. Then he skipped again to anticipate the predictions and ascertain the date and circumstances of his death. Before reaching the final line, however, he had already understood that he would never leave that room, for it was foreseen that the city of mirrors (or mirages) would be wiped out by the wind and exiled from the memory of men at the precise moment when Aureliano Babilonia would finish deciphering the parchments, and that everything written on them was unrepeatable since time immemorial and forever more, because races condemned to one hundred years of solitude did not have a second opportunity on earth." |
Update of Saturday, October 8:
I do not recommend taking very seriously the work of Latin American leftists
(or American academics) who like to use the word "dialectic."
A related phrase does, however, have a certain mystic or poetic charm,
as pointed out by Wikipedia —
"Unity of opposites is the central category of dialectics,
and it is viewed sometimes as a metaphysical concept,
a philosophical concept or a scientific concept."
See also Bullshit Studies.
Comments Off on Paz
Sunday, September 25, 2016
Introduction to Pragmatism
Stanford Encyclopedia of Philosophy
on the origins of Pragmatism:
"Pragmatism had been born in the discussions at
a ‘metaphysical club’ in Harvard around 1870
(see Menand…*). Peirce and James participated
in these discussions along with some other philosophers
and philosophically inclined lawyers. As we have
already noted, Peirce developed these ideas in his
publications from the 1870s."
|
From "How to Make Our Ideas Clear," "The very first lesson that we have a right to demand that logic shall teach us is, how to make our ideas clear; and a most important one it is, depreciated only by minds who stand in need of it. To know what we think, to be masters of our own meaning, will make a solid foundation for great and weighty thought. It is most easily learned by those whose ideas are meagre and restricted; and far happier they than such as wallow helplessly in a rich mud of conceptions. A nation, it is true, may, in the course of generations, overcome the disadvantage of an excessive wealth of language and its natural concomitant, a vast, unfathomable deep of ideas. We may see it in history, slowly perfecting its literary forms, sloughing at length its metaphysics, and, by virtue of the untirable patience which is often a compensation, attaining great excellence in every branch of mental acquirement. The page of history is not yet unrolled which is to tell us whether such a people will or will not in the long-run prevail over one whose ideas (like the words of their language) are few, but which possesses a wonderful mastery over those which it has. For an individual, however, there can be no question that a few clear ideas are worth more than many confused ones. A young man would hardly be persuaded to sacrifice the greater part of his thoughts to save the rest; and the muddled head is the least apt to see the necessity of such a sacrifice. Him we can usually only commiserate, as a person with a congenital defect. Time will help him, but intellectual maturity with regard to clearness comes rather late, an unfortunate arrangement of Nature, inasmuch as clearness is of less use to a man settled in life, whose errors have in great measure had their effect, than it would be to one whose path lies before him. It is terrible to see how a single unclear idea, a single formula without meaning, lurking in a young man's head, will sometimes act like an obstruction of inert matter in an artery, hindering the nutrition of the brain, and condemning its victim to pine away in the fullness of his intellectual vigor and in the midst of intellectual plenty. Many a man has cherished for years as his hobby some vague shadow of an idea, too meaningless to be positively false; he has, nevertheless, passionately loved it, has made it his companion by day and by night, and has given to it his strength and his life, leaving all other occupations for its sake, and in short has lived with it and for it, until it has become, as it were, flesh of his flesh and bone of his bone; and then he has waked up some bright morning to find it gone, clean vanished away like the beautiful Melusina of the fable, and the essence of his life gone with it. I have myself known such a man; and who can tell how many histories of circle-squarers, metaphysicians, astrologers, and what not, may not be told in the old German story?" |
Peirce himself may or may not have been entirely successful
in making his ideas clear. See Where Credit Is Due (Log24,
June 11, 2016) and the Wikipedia article Categories (Peirce).
* Menand, L., 2001. The Metaphysical Club : A Story of
Ideas in America , New York: Farrar, Straus and Giroux
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Friday, September 16, 2016
A Counting-Pattern
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Monday, July 25, 2016
The Retinoid Self
"… which grounds the self" . . .
Popular Mechanics online today —
"Verizon exec Marni Walden seemed to
indicate Mayer's future may still be up in the air."
See also 5×5 in this journal —
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Thursday, July 7, 2016
About Nothing
"For the listener, who listens in the snow,
And, nothing himself, beholds
Nothing that is not there and the nothing that is."
See as well A Riddle for Davos.
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Friday, July 1, 2016
Dead Poet
BBC News today ("4 hours ago" at 2:50 PM ET) —
Poet Sir Geoffrey Hill dies aged 84
|
See also Geoffrey Hill at Poetry Foundation and in this journal.
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Thursday, June 23, 2016
Raiders of the Lost Code
From a web page —
Breaking the Code of the Archetypal Self:
An Introductory Overview of the Research Discoveries
Leading to Neo-Jungian Structural Psychoanalysis
Dr. Moore will introduce his research and discoveries
with regard to the deep structures of the Self.
Tracing the foundations in the tradition of Jung’s
affirmation of the collective unconscious, Moore
will present his “decoding of the Diamond Body,”
a mapping of the deep structures of the Great Code
of the psyche. . . .
From the same web site —
Googling "Jung" + "Diamond Body" shows that
Moore's terminology differs from Jung's.
The octahedron that Moore apparently associates
with his "diamond body" was discussed by Jung
in a different context. See selections from Ch. 14
of Jung's Aion : "The Structure and Dynamics of the Self."
Dr. Moore appears as well in the murder-suicide story
of last night's 11:18 PM ET post.
For the relevance of Aion to "deep structures,"
see Jung + Diamond + Structure in this journal
and, more specifically, "Deep Structure."
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Thursday, May 12, 2016
But Seriously …
Google today released on GitHub an English parser,
Parsey McParseface . From Google Research Blog —
"Today, we are excited to share the fruits of our research
with the broader community by releasing SyntaxNet,
an open-source neural network framework implemented in
TensorFlow that provides a foundation for
Natural Language Understanding (NLU) systems.
Our release includes all the code needed to train new
SyntaxNet models on your own data, as well as
Parsey McParseface , an English parser that we have
trained for you and that you can use to analyze English text."
"While the accuracy is not perfect, it’s certainly high enough
to be useful in many applications. The major source of errors
at this point are examples such as the prepositional phrase
attachment ambiguity described above, which require real
world knowledge (e.g. that a street is not likely to be located
in a car) and deep contextual reasoning. Machine learning
(and in particular, neural networks) have made significant
progress in resolving these ambiguities. But our work is still
cut out for us: we would like to develop methods that can
learn world knowledge and enable equal understanding of
natural language across all languages and contexts."
But seriously …
For some historical background, see (for instance) a book by
Ekaterina Ovchinnikova —
Integration of World Knowledge for
Natural Language Understanding ,
Atlantis Press, Springer, 2012.
A PDF of Chapter 2, "Natural Language Understanding
and World Knowledge," is available for download.
The philosophical background is the distinction between
syntax and semantics . See (for instance) …
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Wednesday, May 11, 2016
By Diction Possessed
Continued from Saturday, May 7, 2016 .
From an obituary in yesterday evening's online New York Times —
"I was writing plays, one-acters, about musicians
who were speakers of the idiom I loved most:
black American male speech, full of curse words,"
he wrote in an autobiographical essay. . . .
The obituary is for a poet who reportedly died on Saturday, May 7.
This journal on that day ("By Diction Possessed") recalled the death
(on Valentine's Day 2015) of an English actor who was the voice of
the Ring in two of the "Lord of the Rings" films —
Backstory from Wikipedia — See Black Speech —
"The only example of 'pure' Black Speech is
the inscription upon the One Ring . . .
-
One Ring to rule them all,
One Ring to find them,
One Ring to bring them all
And in the darkness bind them. "
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Thursday, April 14, 2016
Strange Awards
From a review of a play by the late Anne Meara* —
"Meara, known primarily as an actress/comedian
(half of the team of Stiller & Meara, and mother of
Ben Stiller), is also an accomplished writer for the
stage; her After Play was much acclaimed….
This new, more ambitious piece starts off with a sly
send-up of awards dinners as the late benefactor of
a wealthy foundation–the comically pixilated scientist
Herschel Strange (Jerry Stiller)–is seen on videotape.
This tape sets a light tone that is hilariously
heightened when John Shea, as Arthur Garden,
accepts the award given in Strange's name."
Compare and contrast —
- A figure from yesterday's 1 PM post Black List:
-
The circular device of Doctor Strange on the cover of
Entertainment Weekly , Jan. 8/15 2016:
I of course prefer the Galois I Ching .
* See the May 25, 2015, post The Secret Life of the Public Mind.
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Thursday, April 7, 2016
Plan 9 Continues (Very Slowly)
From the American Mathematical Society today —
|
Verena Huber-Dyson (1923-2016) Huber-Dyson, who worked in group theory and logic, died March 12 at the age of 92. She was born to Swiss parents in Naples and grew up in Athens but moved with her family to Switzerland in 1940 because of the war. Huber-Dyson received her PhD from the University of Zurich in 1947 and moved to the U.S. in 1948 for a post-doctoral fellowship at the Institute for Advanced Study. She held positions at many universities around the world and taught courses on the foundation of mathematics as a philosophy professor at the University of Calgary from 1973 to 1988. Her son, George Dyson, said that her last words were, "This will all go smoothly. Let's get going." She was an AMS member since 1949. Read more about her life. |
See also Huber-Dyson in this journal.
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Monday, March 28, 2016
Easter, 2016
"Minute by minute they live:
The stone's in the midst of all."
— "Easter, 1916"
A Philosophers' Stone
— St. Patrick's Day, 2016
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Tuesday, February 2, 2016
Depth Haiku
From yesterday's 2 PM post —
From "Inception" —
Paraphrase of remarks by "Inception" director Christopher Nolan
at Princeton on June 1, 2015 —
"If you have built castles in the air,
your work need not be lost;
that is where they should be.
Now put the foundations under them.”
— Henry David Thoreau
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Tuesday, January 26, 2016
Ground Plan
The New York Times , reporting yesterday on the death of
a distinguished expert in the field of artificial intelligence,
said that he “laid the foundation for the field.”
Related material:
“A Bad Case of Mixed Metaphors:
Psychiatry, Law, Politics, Society,
and Ezra Pound”
by Arnold M. Ludwig,
American Journal of Psychotherapy
2000 Winter; 54(1): 116-117
From that paper —
“… the conceptual foundation for the field
continues to be primitive.”
See also, in this journal, The Source (Oct. 4, 2014).
An image from that post —
Ground plan for a game of
Noughts and Crosses
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Wednesday, January 20, 2016
Fringe Physics and Beyond
"One day not long ago Oppenheimer stalked
up and down his office and divulged some
startling new discoveries about the 15 fundamental
particles of which the universe is made….
… physicists today are wondering if these particles
are themselves actually the final, stark, immutable
and indivisible foundation stones of the universe
that until now they have been thought to be."
—Lincoln Barnett in LIFE magazine,
Oct. 10, 1949, page 122
Fringe Physics —
"… astrophysics limits the number of fundamental particles to 15…."
— Franklin Potter at FQXi.org on Sep. 27, 2009
"I agree there can't be more than 15 fundamental particles."
— Lawrence B. Crowell at FQXi.org on Sep. 29, 2009
Beyond —
There are, at any rate, 15 "final, stark, immutable* and indivisible*
foundation stones" (namely, 15 points ) of the finite projective
space PG(3,2). See Symplectic in this journal.
For related physics, see posts tagged Dirac and Geometry.
* Update of Jan. 21, 2016 — I was carried away by Barnett's
powerful rhetoric. These adjectives are wrong.
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Monday, November 2, 2015
The Devil’s Offer
This is a sequel to the previous post and to the Oct. 24 post
Two Views of Finite Space. From the latter —
” ‘All you need to do is give me your soul:
give up geometry and you will have this
marvellous machine.’ (Nowadays you
can think of it as a computer!) “
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Saturday, October 31, 2015
Weaving World…
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Wednesday, August 5, 2015
At Zero Dark Thirty…
"I sing the body electric." (See previous post.)
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Wednesday, July 8, 2015
In Memoriam: Stupski
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Design Thinking
This post was suggested in part by last night's post
of 11:14 PM ET, Southern Charm, and by a post
of 11/14 last year, Another Opening, Another Show.
See also Design Thinking at Wikipedia and the following
two quotations —
CHARLESTON COUNTY, SC (WCSC) (today) –
Dr. Gerrita Postlewait's contract for Superintendent
of Charleston County Schools was approved and
signed in a meeting with school board members
Wednesday morning, a school system official says….
From 2006 to 2013, she was the chief K-12 officer for
the Stupski Foundation, a San Francisco-based
education reform nonprofit. [See related page.]
PHILANTHROPY.COM (Aug. 2, 2012) –
Chris Tebben, executive director of Grantmakers for
Education, says the [Stupski] foundation was among
the first to consider how the problem-solving approach
known as “design thinking” could play a role in improving
education.
Related cinematic remarks: Robot Overlords (now on-demand).
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Friday, June 12, 2015
Dickens for Child Buyers
" … yet the dread
Of dying, and being dead,
Flashes afresh to hold and horrify."
— Philip Larkin, "Aubade"
From tonight's New York Times obituaries —
See as well "Child Buyer" in this journal.
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Tuesday, June 2, 2015
Miniature Lowry
A review describes the main character in the 1981 novel
The Knife in My Hands —
"His other peculiar characteristic is a fascination, developed during
his university years, with the Cabala and, like a miniature Lowry,*
he spends much of his time wandering drunkenly through its
labyrinthine mysteries."
AA motto: "Principles before personalities."
* Related material: Back to the Real.
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Wednesday, May 20, 2015
Wednesday, May 6, 2015
Narrative Metaphysics
(Continued from Dec. 13, 2014.)
David Lavery's enthusiasm today for the Marvel Comics
"Infinity Stones" suggests a review of The Foundation Stone
mentioned in the post Narrative Metaphysics of 12/13/2014.
See as well "Many Dimensions" in this journal.
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